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Admin
Brennan should not enter a negative value, since the pedantic definition(1) of "whole number" is "non-negative integer". If it had said "natural number", then zero would also have been excluded.
(1) Well, OK, the one I remember from high school, anyway.
Admin
I would guess that the "lifts" are the things that lift cash from their lockers up to the slot.
Admin
Thanks a lot for the help crosses arms
Admin
It does just say "number" ... so you could write a phrase and calculate the associated Gödel number for it and enter that - assuming that the entry box allows such large numbers to be written.
Admin
with regards to the restaurant question I thought the answer was 42. https://en.wikipedia.org/wiki/42_(number)#The_Hitchhiker.27s_Guide_to_the_Galaxy
Admin
School dumbs stuff down. The non-negative integers are usually called the cardinal numbers, and represent the usual foundation of numbers (the things below it in the foundation stakes are effectively non-numeric; set theory gets a bit odd there if you're not used to it). “Whole numbers” is typically just the integers, negative values included.
Admin
"Whole numbers" is integers, "natural numbers" is "non-negative whole numbers" to a first degree of approximation.
Some old-fashioned texts don't include zero in the natural numbers; it doesn't technically matter which convention you use (as long as you specify which you are using), but zero-based makes the axiomatic construction of the integers a bit easier.
Admin
Addendum 2016-07-29 08:35: Of course, Markdown is the worst at formatting quotes and I can't fix them afterward. And this editing form is the worst.
Addendum 2016-07-29 08:35: And after editing, you get sent back to the article, not your comment. Cool.
Admin
@Zog No, it says "whole number".
Admin
There was a time when not even 1 was considered a number.
(source: Annotations to the book "Carmina mathematica" by H. Cremer)
Defining 0 as a natural number and using 0 as the start index of array has so many advantages over 1 in both cases that I have difficulties to understand why we still use 1 so often. Must have to do with our culture that knows "number zero" only from hour numbers: 00:mm for the first hour of a legal day. (Over here in continental Europe, anyway.)
(Btw, same for sums in mathematics, they're way easier to handle if you get used to run indices from 0 to n-1 instead of from 1 to n. The only drawback is odd looks from mathematicians who have no experience with serious computer programming.)
Admin
By your definition, "natural numbers" would include the set of integers greater than zero, as zero is neither positive nor negative. The set of "whole numbers" includes zero, and the set of integers includes all integers. Those "old fashioned texts" are defining the set of natural numbers correctly, and even the alternate form "counting numbers" indicates the set begins with the value 1. A person does not count a group of items and begin the counting with zero. Instead, (s)he uses the natural or cardinal numbers.
Admin
"...And this editing form is the worst."
Ah you new kids. Its the worst, except for all that came before. You kids don't know how good you have it. In my day on TDWTF, you hit backspace and you never knew how many characters you were going to lose.
Of course, then I took an arrow to the knee.
Admin
In Ireland, lifts use 0 to indicate the ground level, and negative numbers for floors below ground level. I think Ireland's lift companies have been taken over by C programmers. That's a good thing, of course.
Admin
Zero is usually defined as both positive and negative. In order to remove all confusion, mathematicians usually refer to "non-negative" and "non-positive" to mean positive-including-zero and negative-including-zero, and "strictly positive" / "strictly negative" to mean what I will leave it as an exercise for the student to determine.
It is a truism that school-level mathematics text books (and a good many undergraduate-level ones) contain nothing new since Euler. So I don't give a great deal of credence to your modern texts -- they may be modern but their contents are decidedly old-fashioned. Worth bearing in mind that the writers of school-level texts may well not be at the top of their game, so to speak, or they wouldn't be continually rehashing the same tired old 200+-year-old stuff.
There is actually zero need for new school-level and undergraduate-level mathematics texts. The only reason for them is so that failures of mathematicians can make a buck. The price of the damn things is eye-watering (hundreds of dollars in some cases), and the poor schmucks who get lumbered with these courses are being ripped off criminally.
This is one of the reasons mathematics is in such a poor state in (in particular) America.
Admin
"Zero is usually defined as both positive and negative."
That's the first time I've ever heard that.
Admin
Funny, I assumed it was just it was taking the opportunity to advertise a special on shoe inserts.
Admin
My understanding - which clearly isn't universal, so I may just have learned it with a different model - is that 'counting' (also called natural or cardinal) numbers are those with which most people would enumerate something, that is, 1, 2, 3, ... n - in other words, positive integers - while 'whole' (or ordinal) numbers are integers from zero up. I've usually heard zero defined as being neither positive or negative, though I understand that there are some branches of mathematics (topology, maybe?) where it is treated as both for some purposes.
Admin
You want experience? We ARE experience!
Admin
Zeroth time for me.
Admin
Saw that in London, too, this summer. A lift panel with "1","0","-1" and of course "B"
Admin
Same in most places in Germany. We also refer to the floor above the ground floor as the frist floor. AFAIK, that's been so longer than C has existed. So I guess C was invented by European lift-makers.
Admin
It really doesn't matter what convention you use, but mathematicians tend to use a zero-based counting system because it's more convenient than the one-based, which is godawfully clunky. Hence, from what I gather, under such a system it makes sense (convenience, again) to defined zero as both positive and negative.
Those dogmatic know-it-alls who insist that "zero is this" or "zero is that" are obviously not mathematicians because they haven;t grasped the basic fact that a definition can be whatever you want it to be. If it makes sense within the scope of a dissertation for zero to be both positive and negative, then yes, it can be so. It saves stating edge cases: "Let n be a positive integer or zero. Then ..."
For some reason American mathematics appears still to be in the dark ages, and the adherents are still in the medieval mindset where they still believe that definitions have been passed down from Lawd Gahd Almighty, and anyone doing something different for convenience is a heretic. The rest of the world is amused.
Admin
Most places in the world consider the "1st" floor to be the one above ground level. I think the Americas are fairly unique in considering "1" to be ground level.
Admin
If so you end up with a count of 1 when counting the number of persons in an empty room...
Admin
I'm sure glad the math textbooks are old fashion. I wouldn't want my kids to take post-modern math where 2 + 2 is whatever you feel it should be.
Admin
The bullshit and blather of the stupid person trying to sound clever, when in fact you just end up sounding like a bit of a prick.
Admin
No. This is standard usage: "Whole numbers" means 1, 2, 3, ... . "Natural numbers" means 0, 1, 2, ... . Integers means ..., -2, -1, 0, 1, 2, ...
But you are free to define them any way you want. Just don't expect everyone to understand you.
Admin
Look, it's really simple.
Natural numbers are those which occur naturally, and can be consumed by almost anybody. Whole numbers are those with husks, and are supposed to be healthier. Whole numbers may or may not be natural, depending on where you grow them. Numbers can be positive, negative, non-positive, non-negative, and they are suitable for different consumption styles.
Real numbers are those which are to be sold against a prescription by real mathematicians, though some of them can be sold without it to adults, the presumption being that adults are rational. (and of course fewer of them are just the natural numbers.)
Not being satisfied by the reality of real numbers, some mathematicians let their imagination run astray, and it becomes complex when they mix facts with fiction.
Admin
Actually, mathematicians rarely use the term "whole numbers", at least not past grade-school. It's usually "integers" and / or "positive integers" and / or "non-negative integers" -- even the term "natural numbers" tends to be restricted nowadays to the fields of axiomatics and such like, where it is important to understand exactly how they have been constructed.
Admin
VHDL has a "Natural" as a subtype of Integer with a range of [0 .. Integer'high].
Admin
So what are 'organic' numbers then?
Admin
There is one useful purpose for new grade-school math textbooks: different learning methods. Students have different ways that they learn best, so having textbooks that present the material in a manner appropriate to a student's best learning method means the student has a stronger grasp of the subject at an earlier age. The best school textbooks (in any subject) are co-written by an expert in the field and an educator working together.
Of course, many textbooks are written in a manner that teaches rote memorization of facts with no understanding of the underlying concepts. These produce students who score well on standardized tests, but they quickly fall behind when more advanced concepts begin to be introduced.
Admin
The "Install Certificate" button only appears in IE when you're running as Administrator, but fortunately only summons a wizard that allows you to choose the destination certificate store.
Admin
I would have rated them as a 9/10, but had to round that down to 0 :(
Admin
In the French language there's just one word you use for "whole" and "integer". It exists in English, as the variant "entire". (then, "integral" exists in both French and English).
So let's say the word is "integer" and is both a noun and adjective, then you may have :
Admin
One of my favorite weird memories was of the early web in the 1990s, when password constraints on forms were in their infancy. I'm not overstating it when I say that this one form was a real-life predecessor of "The Password Game", thirty years earlier.
This stuff is more rare now but has a rich history.
Admin
Unrelated, but after forty years of working with computers, I kind of wish that someone had said from on high "All integer types are signed, deal with it". The sheer number of issues I've seen in that time from signed/unsigned conversion and confusion has dwarfed any benefit that you would otherwise get from distinct types.